This readily implies that the corresponding non-singular DFT ansatz (REF ) solves the DFT Einstein equations \({G_{AB}+{\cal J}_{AB}\,\Lambda _{\scriptscriptstyle {\rm {DFT}}}=0}\)  everywhere even at the non-Riemannian points of \({F=0}\) . It also means that all the \(\mathbf {O}(D,D)\) -symmetric DFT curvatures are trivially regular [1]}. Similarly, while the conventional dilaton \(\phi \)  diverges as \({F\rightarrow 0}\) , the DFT dilaton \(d\)  remains finite, c.f. (REF ), hence so does the \(\mathbf {O}(D,D)\) -symmetric version of Fradkin–Tseytlin term [2]} in doubled string actions [3]}, [4]}.
